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 Jun 30 comment Cholesky decomposition and variance It actually may be better to write it as just $Cov(A+BZ)=B^TCov(Z)B$, since of course adding a constant has no effect on variance and so $Cov(A)=0$, a reference can be found here: en.wikipedia.org/wiki/…. Jun 30 comment Cholesky decomposition and variance $Cov(A + BZ) = Cov(A) + B^TCov(Z)B$. This is a direct result of the linearity of expectation. However it should be clear right away that it definitely can't be just $B$, since the covariance matrix must be positive semi-definite. Jun 30 comment When trying to learn analysis from bottom up, what numbers should I first construct? mathematicians aren't interested in foundations Jun 23 comment Default positive/(non-negative) probability distribution It appears to be a generalization of the exponential distribution for the specification of higher moments. There is no 'equivalent' distribution in the absolute sense, it appears to be equivalent in the sense of maximizing entropy. Whether or not maximizing entropy is the right call for capturing your lack of prior knowledge in the model is entirely up to your own judgement of the problem. Jun 23 comment Default positive/(non-negative) probability distribution Note that assuming a normal distribution also requires estimates for the mean and variance. I'm sure there is info online on the average volume of oxygen inhaled per minute/hour whatever. Jun 23 comment Default positive/(non-negative) probability distribution If you have some data to calculate the sample mean and sample variance, then you might take a look at this answer: stats.stackexchange.com/questions/83069/…. For a given mean and variance, the normal distribution maximizes entropy, this answer appears to provide the equivalent for a distribution with strictly nonnegative support. Jun 23 comment What math preparation is needed before reading the mathematical method in financial markets? measure theoretic probability, stochastic calculus, stochastic differential equations, looking at the table of contents that book is no joke. Even if you knew all that stuff I wouldn't recommend that book for a first pass. Jun 22 comment Does there exist a function $F(x)$, so that $F'(x)$ is not Riemann integrable? man wtf, are these objects just anomalies of the real line, why would the universe allow such abominations to exist? Jun 16 comment Solving a matrix equation using numerical optimization You can without loss of generality assume that $A$ is symmetric. if $A$ is not positive semi-definite then the function is not bounded below and so the minimum is $-\infty$. Jun 14 comment Density function of a transformation $P(Y < a) = P(X^3 < a ) = P(X < \sqrt[3]{a})$ Jun 13 comment Decomposition of an asymmetric 'postive definite' matrix by asymmetric do you mean not symmetric or antisymmetric? Also you use $\succcurlyeq$ but you say positive definite, which do you mean? Jun 13 comment Differentiation of a complex matrix en.wikipedia.org/wiki/Matrix_calculus#Matrix-by-scalar Jun 7 comment Is this series convergent? do the terms go to zero? Jun 6 comment Given a biased coin $P(X=0)=.75$, can someone show me a compression scheme that beats 1 bit wow so simple, I was sure bothering with '0' '1' combos would be a mistake since they are low probability but mapping them to the longer code lengths makes sense. Thanks! Jun 6 comment Hessian Matrix and critical point look at the eigenvalues of the matrix, specifically are they positive, negative, a mixture of both? Jun 5 comment Problem for number theory $\sum_{k=1}^nkx_k = \sum_{j=1}^n\sum_{k=j}^nx_k$ this might help Jun 2 comment How to solve $\min \limits_{\mathbf{x}} \| \mathbf{Ax}-\mathbf{b} \|^2$? if A is non-negative you need to include that as one of the constraints Jun 2 comment Cost function for very sparse, real-valued data induced l1 norm then round the smallest 95% to zero, this might be better migrated to stats stack exchange though Jun 1 comment What is the first order approximation to a differentiable function $F:M_{n\times n}(\mathbb{R})\to\mathbb{R}$ shouldn't $\epsilon(h)$ depend on $x$ as well? Jun 1 comment Derivative of $(\ln x)^e$ $e^{ln(x)}$ is x, this is just the natural log raised to a number.